Newform orbit 123.5.p.a

• Label: 123.5.p.a
• Level: $123$
• Weight: $5$
• Character orbit: 123.p
• Analytic conductor: $12.715$
• Analytic rank: $0$
• Dimension: $448$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	123.p (of order \(40\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.7145054593\)
Analytic rank:	\(0\)
Dimension:	\(448\)
Relative dimension:	\(28\) over \(\Q(\zeta_{40})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 448 q+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−3.46293	−	6.79638i	−1.98848	+	4.80062i	−24.7943	+	34.1264i	5.53615	+	34.9539i	39.5128	−	3.10972i	−8.10513	−	0.637887i	197.255	+	31.2422i	−19.0919	−	19.0919i	218.388	−	158.668i
7.2	−3.46250	−	6.79553i	1.98848	−	4.80062i	−24.7858	+	34.1147i	1.62389	+	10.2528i	−39.5079	+	3.10934i	72.2512	+	5.68630i	197.122	+	31.2211i	−19.0919	−	19.0919i	64.0506	−	46.5355i
7.3	−2.99910	−	5.88606i	−1.98848	+	4.80062i	−16.2465	+	22.3614i	−4.47030	−	28.2243i	34.2204	−	2.69320i	−41.2480	−	3.24628i	75.9496	+	12.0292i	−19.0919	−	19.0919i	−152.723	+	110.960i
7.4	−2.83558	−	5.56515i	1.98848	−	4.80062i	−13.5258	+	18.6166i	4.14995	+	26.2018i	−32.3546	+	2.54637i	−58.9264	−	4.63761i	43.2533	+	6.85065i	−19.0919	−	19.0919i	134.049	−	97.3924i
7.5	−2.69674	−	5.29266i	1.98848	−	4.80062i	−11.3352	+	15.6016i	−2.12273	−	13.4024i	−30.7705	+	2.42169i	5.75198	+	0.452691i	19.2710	+	3.05222i	−19.0919	−	19.0919i	−65.2099	+	47.3778i
7.6	−2.38264	−	4.67620i	−1.98848	+	4.80062i	−6.78526	+	9.33911i	1.77954	+	11.2356i	27.1865	−	2.13962i	33.3439	+	2.62422i	−23.0993	−	3.65857i	−19.0919	−	19.0919i	48.2998	−	35.0918i
7.7	−2.02657	−	3.97738i	1.98848	−	4.80062i	−2.30796	+	3.17663i	−7.34596	−	46.3806i	−23.1237	+	1.81987i	−11.4783	−	0.903360i	−53.2314	−	8.43102i	−19.0919	−	19.0919i	−169.586	+	123.211i
7.8	−2.01755	−	3.95967i	−1.98848	+	4.80062i	−2.20389	+	3.03339i	2.16160	+	13.6478i	23.0207	−	1.81177i	−42.8674	−	3.37374i	−53.7715	−	8.51657i	−19.0919	−	19.0919i	49.6796	−	36.0944i
7.9	−1.43873	−	2.82366i	1.98848	−	4.80062i	3.50143	−	4.81930i	2.68038	+	16.9233i	−16.4162	+	1.29198i	75.6853	+	5.95657i	−68.7266	−	10.8852i	−19.0919	−	19.0919i	43.9292	−	31.9165i
7.10	−1.33078	−	2.61180i	1.98848	−	4.80062i	4.35403	−	5.99280i	5.90554	+	37.2861i	−15.1845	+	1.19505i	−3.92365	−	0.308798i	−67.7696	−	10.7336i	−19.0919	−	19.0919i	89.5250	−	65.0437i
7.11	−1.14432	−	2.24586i	−1.98848	+	4.80062i	5.67014	−	7.80428i	3.79965	+	23.9901i	13.0570	−	1.02761i	68.7674	+	5.41211i	−63.8488	−	10.1127i	−19.0919	−	19.0919i	49.5304	−	35.9859i
7.12	−0.962920	−	1.88984i	−1.98848	+	4.80062i	6.76030	−	9.30475i	−6.44256	−	40.6767i	10.9871	−	0.864706i	4.88732	+	0.384640i	−57.6125	−	9.12492i	−19.0919	−	19.0919i	−70.6687	+	51.3438i
7.13	−0.646113	−	1.26807i	1.98848	−	4.80062i	8.21403	−	11.3056i	−2.01043	−	12.6933i	−7.37229	+	0.580212i	−55.9427	−	4.40278i	−42.1341	−	6.67339i	−19.0919	−	19.0919i	−14.7971	+	10.7507i
7.14	−0.140677	−	0.276094i	−1.98848	+	4.80062i	9.34813	−	12.8666i	−0.000529835	−	0.00334525i	1.60515	−	0.126328i	32.6540	+	2.56992i	−9.76428	−	1.54651i	−19.0919	−	19.0919i	−0.000849066	0	0.000616882i
7.15	0.124359	+	0.244068i	−1.98848	+	4.80062i	9.36046	−	12.8836i	6.81545	+	43.0310i	−1.41896	+	0.111675i	−76.8510	−	6.04831i	8.63736	+	1.36802i	−19.0919	−	19.0919i	−9.65495	+	7.01473i
7.16	0.374021	+	0.734057i	1.98848	−	4.80062i	9.00562	−	12.3952i	−4.96658	−	31.3577i	4.26766	−	0.335872i	67.1687	+	5.28629i	25.4864	+	4.03665i	−19.0919	−	19.0919i	21.1608	−	15.3742i
7.17	1.08504	+	2.12950i	1.98848	−	4.80062i	6.04709	−	8.32310i	4.79631	+	30.2827i	12.3805	−	0.974366i	31.7374	+	2.49779i	62.0545	+	9.82847i	−19.0919	−	19.0919i	−59.2829	+	43.0716i
7.18	1.20381	+	2.36261i	1.98848	−	4.80062i	5.27179	−	7.25600i	−1.74351	−	11.0081i	13.7358	−	1.08103i	−44.8798	−	3.53212i	65.3929	+	10.3572i	−19.0919	−	19.0919i	23.9089	−	17.3709i
7.19	1.23172	+	2.41739i	−1.98848	+	4.80062i	5.07791	−	6.98915i	−1.22116	−	7.71011i	−14.0542	+	1.10609i	−24.2923	−	1.91184i	66.0253	+	10.4574i	−19.0919	−	19.0919i	17.1342	−	12.4488i
7.20	1.26061	+	2.47408i	−1.98848	+	4.80062i	4.87261	−	6.70657i	−2.47200	−	15.6076i	−14.3838	+	1.13203i	−35.1533	−	2.76662i	66.6158	+	10.5509i	−19.0919	−	19.0919i	35.4982	−	25.7910i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
41.h	odd	40	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	123.5.p.a	✓	448
41.h	odd	40	1	inner	123.5.p.a	✓	448

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
123.5.p.a	✓	448	1.a	even	1	1	trivial
123.5.p.a	✓	448	41.h	odd	40	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(123, [\chi])\).